NumberField.places() does not return homomorphisms to RIF/CIF

[mathehertogh]

For K a number field, K.places() returns homomorphisms into RealField(106) and ComplexField(53). For example:

sage: K.<a> = NumberField(x^3-2)
sage: K.places()
[Ring morphism:
   From: Number Field in a with defining polynomial x^3 - 2
   To:   Real Field with 106 bits of precision
   Defn: a |--> 1.259921049894873164767210607278,
 Ring morphism:
   From: Number Field in a with defining polynomial x^3 - 2
   To:   Complex Field with 53 bits of precision
   Defn: a |--> -0.629960524947437 + 1.09112363597172*I]

While the documentation reads:

   Return the collection of all infinite places of self.

   By default, this returns the set of real places as homomorphisms
   into RIF first, followed by a choice of one of each pair of complex
   conjugate homomorphisms into CIF.

   On the other hand, if prec is not None, we simply return places
   into RealField(prec) and ComplexField(prec) (or RDF, CDF if
   prec=53).

I checked the implementation and it would be a simple and quick fix to actually return morphisms into RIF/CIF. But I don't know if that is what is actually wanted?
Quite some code now uses this function the way it currently is.

Either the documentation should be updated, or the code should be adjusted. I am willing to do it, but don't know which of the two options.

Component: number fields

Issue created by migration from https://trac.sagemath.org/ticket/31604

[mkoeppe]

comment:1

Moving to 9.4, as 9.3 has been released.